Also do some research into "prepared piano" to understand how some of the timbres are achieved. Pretty sure there is some "preparation" done to the hammers/strings on the Disklavier in these songs.
[0]: My favorite - https://www.youtube.com/watch?v=97FBWB4vv3s
I didn't listen carefully to the whole track, but I think you could handle what I did hear that way. Not certain that would work here, just thought I'd point out that there are options beyond your fingers for pushing keys.
J. S. Bach is reputed to have held a stick in his mouth to have an additional note on tap - much more practical and playable than my stupid nose trick. If you used a forked stick or a crafted tool you could easily get more than one note, for that matter.
http://www.storycompositions.com/2008/07/rare-stories-about-... (see section "His Music Is Terrible")
(I've also used my face to move modwheels while holding dense chords with both hands, but that's not really relevant to piano technique.)